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The estimation of implied volatility from the Black-Scholes model: some new formulas and their applications


  • Steven Li


This paper provides a more accurate formula for estimating the implied volatilities for at-the-money calls than the existing formula as developed previously by Brenner and Subrahmanyam (1988). New formulas are also given for estimating the implied volatilities of in- or out-of-the-money calls. These formulas are derived mathematically and assessed by using numerical tests. All the new formulas are easy to use and accurate for a wide range of option moneyness and time to expiration.

Suggested Citation

  • Steven Li, 2003. "The estimation of implied volatility from the Black-Scholes model: some new formulas and their applications," School of Economics and Finance Discussion Papers and Working Papers Series 141, School of Economics and Finance, Queensland University of Technology.
  • Handle: RePEc:qut:dpaper:141

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    References listed on IDEAS

    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    2. Chance, Don M, 1996. "A Generalized Simple Formula to Compute the Implied Volatility," The Financial Review, Eastern Finance Association, vol. 31(4), pages 859-867, November.
    3. Chambers, Donald R & Nawalkha, Sanjay K, 2001. "An Improved Approach to Computing Implied Volatility," The Financial Review, Eastern Finance Association, vol. 36(3), pages 89-99, August.
    4. N/A, 1996. "Note:," Foreign Trade Review, , vol. 31(1-2), pages 1-1, January.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    More about this item


    options; implied volatility; implied standard deviation;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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